Rolling bearing collision friction characteristic analysis method considering variable-speed variable-load working conditions

Abstract

The invention relates to the technical field of rolling bearing collision friction characteristic analysis, in particular to a rolling bearing collision friction characteristic analysis method considering variable-speed variable-load working conditions. Comprising the following steps: step 1, selecting a cylindrical roller bearing and searching bearing parameters; step 2, establishing a cylindrical roller bearing system dynamic model; step 3, calculating the rigidity and damping of the cylindrical roller bearing system; step 4, considering three degrees of freedom of a retainer in planar motion, and establishing a multi-degree of freedom dynamic differential equation; 5, solving a multi-degree-of-freedom dynamic differential equation by using a fixed-step-length four-order Runge-Kutta method; step 6, performing iterative calculation on the motion differential equation within time t by using a four-order fixed-step Runge-Kutta method; and step 7, analyzing collision and friction characteristics of the retainer. The invention provides a method for calculating collision force and friction force between the rolling body and the retainer under the condition that a viscous damping effect exists between the rolling body and the retainer.

Description

Technical Field

[0001] This invention relates to the field of rolling bearing collision friction characteristic analysis technology, and specifically to a method for analyzing the collision friction characteristics of rolling bearings considering variable speed and load conditions. Background Technology

[0002] Rolling bearings are among the key components in rotating machinery, and their operating condition directly affects the performance and reliability of the equipment. Variable speed and load conditions deteriorate the internal contact conditions of the bearing, and in severe cases, accelerate bearing wear, thus significantly impacting bearing accuracy and lifespan. Investigating the cage collision friction mechanism under variable speed and load conditions is of great research significance for reducing cage fracture and wear, optimizing bearing operating accuracy, and extending bearing life.

[0003] Current methods for calculating the collision force between rolling elements and the cage do not consider the viscous damping effect between them, nor do they adequately account for the influence of the hydrodynamic pressure of lubricating oil on the cage's dynamic characteristics, leading to significant deviations between the calculated results and actual values. Furthermore, while existing technologies have extensively studied the collision friction characteristics of rolling bearing cages, these studies primarily focus on steady-state operating conditions. In reality, absolutely stable operating conditions do not exist. In most rotating machinery, due to numerous physical factors, variable speed and load conditions frequently occur. However, research on the cage's collision friction characteristics under variable speed and load conditions, such as speed fluctuations, acceleration / deceleration, and load fluctuations, is limited. Summary of the Invention

[0004] In response to the problems raised in the background art, the present invention provides a method for analyzing the collision friction characteristics of rolling bearings considering variable speed and load conditions. The present invention will be further described below.

[0005] A method for analyzing the collision friction characteristics of rolling bearings considering variable speed and load conditions includes the following steps:

[0006] Step 1: Select the cylindrical roller bearing and find the bearing parameters:

[0007] Step 2: Based on the dynamics theory of rolling bearings, considering the hydrodynamic pressure of the lubricating oil, the viscous damping effect between the rolling elements and the cage, and the vibration coupling effect between the outer ring and the bearing housing, a dynamic model of the cylindrical roller bearing system is established:

[0008] Step 3: Based on the basic parameters of cylindrical roller bearings, considering the influence of elastohydrodynamic lubrication, calculate the stiffness and damping of the cylindrical roller bearing system using the finite element method, Hertzian contact theory, and elastohydrodynamic lubrication theory:

[0009] Step 4: Consider the three degrees of freedom of the cage in planar motion and establish the multi-degree-of-freedom dynamic differential equations;

[0010] Step 5: Solve the multi-degree-of-freedom dynamic differential equations using the fixed-step fourth-order Runge-Kutta method;

[0011] Step 6: Use the fourth-order fixed-step Runge-Kutta method to iteratively calculate the differential equation of motion within time t;

[0012] Step 7: Analyze the impact friction characteristics of the cage.

[0013] Preferably, in step 1, before performing rolling bearing dynamics modeling, it is necessary to select the cylindrical roller bearing model and find the parameters of the cylindrical roller bearing under study. The basic parameters include: outer raceway radius, inner raceway radius, pitch circle radius, number of rolling elements, rolling element diameter, radial clearance, total mass of inner ring and shaft, cage pocket clearance, cage moment of inertia, etc.

[0014] Preferably, in step 2, the cylindrical roller bearing system is dynamically modeled using springs, damping, and concentrated mass. An equivalent spring and equivalent damper system is used to simulate the mutual contact between the rolling elements, raceways, and cage. The interaction between the cage and the guide raceway is considered as hydrodynamic pressure and Hertzian contact. The inner ring and the shaft are considered as a whole, and the outer ring is fixed to the bearing housing. The bearing housing is considered as an elastic support with stiffness and damping. The vibration coupling effect between the outer ring and the bearing housing, the hydrodynamic pressure of the lubricating oil, and the viscous damping effect between the rolling elements and the cage are considered. Based on the rolling bearing dynamics theory, a dynamic model of the shaft-cylindrical roller bearing-bearing housing system is established.

[0015] Preferably, in step 3, the stiffness of the roller bearing system includes: the support stiffness k between the bearing housing and the outer ring of the bearing. h The total contact stiffness k between the bearing outer ring and the rolling elements after elastohydrodynamic lubrication was considered. out Total contact stiffness k between the bearing inner ring and the rolling elements in Contact stiffness k between rolling elements and cage c .

[0016] Preferably, in step 4, based on Newton's second law of motion and the established dynamic model of the roller bearing system, the dynamic differential equations of each component of the roller bearing system are established as follows:

[0017] ①The differential equation of motion for the outer circle is:

[0018]

[0019] In the formula: mo is the mass of the outer ring; Noj is the contact force between the rolling element and the outer ring; foj is the frictional force between the rolling element and the outer ring; θj is the time-varying position angle of the j-th rolling element; K h ch These are the stiffness coefficient and damping coefficient between the outer ring and the bearing housing, respectively. and and x o With y o These represent the acceleration, velocity, and displacement of the outer ring in the X and Y directions, respectively.

[0020] ②The differential equation of motion for the inner circle is:

[0021]

[0022] Where: m i W is the mass of the inner ring (including the shaft); N is the radial load; ij ρ is the contact force between the rolling element and the inner ring; fij is the frictional force between the rolling element and the inner ring; c is the system damping. and and These represent the acceleration and velocity of the inner ring in the X and Y directions, respectively.

[0023] ③The differential equation of cage motion is:

[0024]

[0025] In the formula: J c To maintain the moment of inertia of the cage's rotation; To maintain the angular acceleration of the cage rotation; N cj1 With N cj2 These are the impact contact forces between the rolling element and the front and rear ends of the cage pocket, respectively; R m M is the bearing pitch circle radius; c The frictional torque acting on the cage; m c To maintain rack quality; and and These represent the acceleration and velocity of the cage in the X and Y directions, respectively; G c To maintain the weight of the cage; N cx With N cy Let F be the resultant force (normal contact force and tangential friction force) of the rolling elements acting on the cage, decomposed along the X and Y axes of the inertial coordinate system; c is the system damping; F cx With F cy These are the forces decomposed into forces along the X and Y axes of the inertial coordinate system, representing the resultant force of the guide ring acting on the cage. ωc To maintain the dynamic imbalance force; To maintain the rotation angle of the cage;

[0026] ④ The differential equation of motion for the rolling element is:

[0027]

[0028] Where: m r G is the mass of the rolling element; r For rolling gravity; F ωj c is the centrifugal force of the rolling element; c is the system damping. These are the accelerations of the j-th rolling element in the vertical X and horizontal Y directions of the inertial coordinate system, respectively. and Let X and Y be the velocities of the j-th rolling element along the vertical X and horizontal Y directions of the inertial coordinate system, respectively. These are the angular accelerations of the rolling element's revolution and rotation, respectively; J r R is the moment of inertia of the rolling element's rotation. r f is the radius of the rolling element; cj1 and f cj2 These are the frictional forces between the rolling elements and the front and rear ends of the cage pockets, respectively.

[0029] Preferably, in step 5, the parameters in the dynamic equations of each component of the cylindrical roller bearing system are determined, and the dynamic differential equations are solved using the fixed-step fourth-order Runge-Kutta method to obtain the collision force and friction force between the rolling elements and the cage.

[0030] Preferably, in step 6, the fourth-order fixed-step Runge-Kutta method is used to iteratively calculate the motion differential equation within time t. Before the calculation, the bearing system is assigned initial values. If t has not reached the termination time T, the relative positions of each part are updated, and t = t + Δt is set, and S2-S7 are repeated. If t reaches the termination time T, the slippage dynamic characteristics of each bearing component at each moment are output, and the time step for solving is set to Δt = 5 × 10-6 s, and the solution termination time is T = 2 s.

[0031] Preferably, in step 7, the amplitude, frequency, and distribution changes of the collision force and friction force between the rolling elements and the cage under variable speed and load conditions are analyzed.

[0032] Beneficial effects: Compared with the prior art, the present invention:

[0033] (1) This invention provides a method for calculating the collision force and friction force between the rolling element and the cage when there is a viscous damping effect between the rolling element and the cage;

[0034] (2) The present invention also provides a method for calculating the interaction force between the cage and the guide ring under the hydrodynamic pressure of lubricating oil and Hertzian contact action;

[0035] (3) The present invention also provides a dynamic modeling method for cages with three degrees of freedom in planar motion, which makes cage simulation closer to actual working conditions and is conducive to conducting cage collision friction characteristic analysis;

[0036] (4) The present invention also provides an iterative calculation method for the dynamic model of rolling bearing under the vibration coupling effect of the outer ring and the bearing housing, which determines the collision force and friction force between the rolling element and the cage at each moment, and provides a certain theoretical basis for the performance evaluation of rolling bearing. Attached Figure Description

[0037] Figure 1 : A schematic diagram of a method for analyzing the collision friction characteristics of rolling bearings considering variable speed and load conditions according to the present invention;

[0038] Figure 2 : A schematic diagram of the dynamic model of the rolling bearing system of the present invention;

[0039] Figure 3 The relative positional relationship between the rolling element and the raceway after being loaded according to the present invention;

[0040] Figure 4 : Schematic diagram of the position and force relationship between the rolling element and the cage in the inertial frame of the present invention;

[0041] Figure 5 : Schematic diagram of the interaction between the cage and the guide ring under hydrodynamic pressure conditions of the present invention;

[0042] Figure 6 : Schematic diagram of the interaction between the cage and the guide ring in the Hertz contact state of the present invention. Detailed Implementation

[0043] Next, we will combine the appendix Figure 1-6 A specific embodiment of the present invention will be described in detail below.

[0044] A method for analyzing the collision friction characteristics of rolling bearings considering variable speed and load conditions includes the following steps:

[0045] Step 1: Select the cylindrical roller bearing and find the bearing parameters:

[0046] Before performing dynamic modeling of rolling bearings, it is necessary to select the cylindrical roller bearing model and find the parameters of the cylindrical roller bearing under study. The basic parameters include: outer raceway radius, inner raceway radius, pitch circle radius, number of rolling elements, rolling element diameter, radial clearance, total mass of inner ring and shaft, cage pocket clearance, cage moment of inertia, etc.

[0047] Step 2: Based on the dynamics theory of rolling bearings, considering the hydrodynamic pressure of the lubricating oil, the viscous damping effect between the rolling elements and the cage, and the vibration coupling effect between the outer ring and the bearing housing, a dynamic model of the cylindrical roller bearing system is established:

[0048] A dynamic model of the cylindrical roller bearing system is performed using springs, dampers, and concentrated mass. An equivalent spring and damper system is used to simulate the contact interactions between the rolling elements, raceways, and cage. The interaction between the cage and guide raceways is considered as hydrodynamic pressure and Hertzian contact. The inner ring and shaft are treated as a single unit, with their total mass defined as m. i The outer ring is fixed on the bearing housing, and its mass is defined as m. o The bearing housing is considered as an elastic support with stiffness and damping, taking into account the vibration coupling effect between the outer ring and the bearing housing. A planar coordinate system is established by considering the radial motion of the bearing, i.e., the vertical X direction and the horizontal Y direction. The effects of the hydrodynamic pressure of the lubricating oil and the viscous damping effect between the rolling elements and the cage are further considered. Based on the theory of rolling bearing dynamics, a dynamic model of the shaft-cylindrical roller bearing-bearing housing system is established.

[0049] Step 3: Based on the basic parameters of cylindrical roller bearings, considering the influence of elastohydrodynamic lubrication, calculate the stiffness and damping of the cylindrical roller bearing system using the finite element method, Hertzian contact theory, and elastohydrodynamic lubrication theory:

[0050] The stiffness in a roller bearing system includes: the supporting stiffness k between the bearing housing and the outer ring of the bearing. h The total contact stiffness k between the bearing outer ring and the rolling elements after elastohydrodynamic lubrication was considered. out Total contact stiffness k between the bearing inner ring and the rolling elements in Contact stiffness k between rolling elements and cage c .

[0051] (1) Calculate the support stiffness between the bearing housing and the outer ring of the bearing:

[0052] Considering the complexity of the bearing housing geometry, the static finite element method is used to calculate the stiffness. The calculation is performed using ANSYS Workbench software, the deformation at the contact point is extracted, and the relationship between load and deformation is obtained. The contact stiffness between the outer ring and the bearing housing is k. h .

[0053] (2) Calculate the total contact stiffness between the rolling elements and the inner and outer raceways of the bearing:

[0054] Because of the lubricating oil inside the bearing, the stiffness between the rollers and the inner and outer raceways is an equivalent combination of the contact stiffness and oil film stiffness inherent in the material itself. For cylindrical roller bearings, the contact between the rolling elements and the raceways is line contact. According to Hertzian contact theory, the contact deformation between the rollers and the raceways is as follows:

[0055]

[0056] In the formula: W is the radial force, L e R is the effective contact length between the roller and the raceway. r and R i / o Let E1 and E2 be the radii of the roller and raceway, respectively, E1 and E2 be the elastic moduli of the roller and raceway materials, respectively, and υ1 and υ2 be the Poisson's ratios of the roller and raceway materials, respectively. r Let be the width dimension of the contact surface, and its expression is:

[0057]

[0058] By solving the two equations above, the contact stiffness k between the roller and the inner and outer raceways can be obtained. i and k o .

[0059] The minimum oil film thickness at the center of the contact area between the roller and the inner and outer raceways is derived from the elastohydrodynamic lubrication theory, which is given by the following formula:

[0060]

[0061] In the formula: α o η0 is the pressure index of viscosity, η0 is the dynamic viscosity at atmospheric pressure, u is the average surface velocity, R is the equivalent radius of curvature of the two cylinders, E0 is the equivalent elastic modulus, q is the load applied per unit contact length, and the subscripts i and o represent the oil film thickness of the inner and outer raceways, respectively. Oil film stiffness (k0) oil i(o) The stiffness is calculated from the definition of stiffness:

[0062]

[0063] Total contact stiffness k in and k out Defined as:

[0064]

[0065] (3) Calculate the contact stiffness between the rolling elements and the cage:

[0066] The contact stiffness between the rolling elements and the cage can be determined by the following formula:

[0067]

[0068] In the formula: E is the elastic modulus, l is the effective contact length between the rolling element and the cage pocket, and υ is Poisson's ratio.

[0069] Damping in a roller bearing system includes the damping coefficient c between the bearing housing and the outer ring of the bearing. h The damping coefficient c between the bearing outer ring and the rolling elements o The damping coefficient c between the bearing inner ring and the rolling elements i The damping coefficient c between the rolling elements and the cage c .

[0070] (1) In the established model, assuming that the bearing housing damping is hysteretic, the formula for calculating the equivalent viscous damping of the outer ring and bearing housing is:

[0071]

[0072] In the formula: c h For the equivalent viscous damping of the outer ring and bearing housing, η h k is the power consumption coefficient for the outer ring and bearing housing. h ω represents the support stiffness between the bearing housing and the outer ring of the bearing. ext The excitation frequency.

[0073] (2) The damping between the rolling element and the inner ring raceway, the rolling element and the outer ring raceway, and the rolling element and the cage can be determined by the following formula:

[0074] c i(o) = (0.25-2.5)×10 -5 k in(out)

[0075] c c =(0.25-2.5)k c

[0076] Step 4: Consider the three degrees of freedom of the cage in planar motion, and establish the multi-degree-of-freedom dynamic differential equations:

[0077] When a cylindrical roller bearing is subjected to a radial load, a nonlinear Hertzian contact force is generated between the rolling elements and the inner and outer ring raceways due to compression. When the outer ring is fixed and the inner ring rotates, the rolling elements rotate under the action of raceway friction, causing the cage to revolve around the bearing center. Due to the difference between the rolling element's revolution speed and the cage's rotation speed, a nonlinear intermittent collision occurs between the rolling elements and the cage. Based on Hertzian contact theory, the load-displacement deformation relationship of a rolling bearing under line contact conditions is:

[0078] N ij(oj) =k in(out) (δ jin(out) ) n

[0079] In the formula: n is the bearing load deformation index, for cylindrical roller bearings n = 10 / 9; δ j in and δ j out Let be the normal contact deformation between the j-th rolling element and the inner raceway and the outer raceway, respectively, and their expressions are as follows:

[0080]

[0081] Where, "+" indicates that the value inside the parentheses is set to 0 when it is less than 0; r0 is the radial clearance; d rj Let be the radial displacement of the j-th rolling element.

[0082] θ j Let the position angle of the j-th roller be expressed as:

[0083] θ j =(2π / N) b (j-1)+θ rj

[0084] Where, N b Let j be the number of rollers, from 1 to N. b ;θ rj The angle of revolution of the roller.

[0085] When the rolling element enters the sliding region of the bearing load area, the sliding friction between the rolling element and the raceway causes the rolling element to rotate. The resulting sliding friction can be expressed as:

[0086] f ij =μ i N ij

[0087] f oj =μ o N oj

[0088] Where, μ i and μ o These are the coefficients of friction between the rolling element and the inner and outer rings, respectively.

[0089] Taking into account the relative displacement between the roller and the cage and the circumferential pocket clearance of the cage, the local contact deformation δ between the roller and the cage is... cj It can be represented as:

[0090] δ cj =(Z cj -p c )

[0091]

[0092] Among them, Z cj p represents the relative displacement between the rolling elements and the cage. c To maintain the clearance of the bracket pocket; x c y c To maintain the displacement of the frame in the radial plane.

[0093] Considering the viscous damping effect, the nonlinear impact force N between the roller and the cage cj and frictional force f cj It can be represented as:

[0094]

[0095] f cj =u c N cj

[0096] Where, k c v represents the contact stiffness between the roller and the cage. rc μ represents the relative circumferential velocity between the roller and the cage. e u is the correlation coefficient of viscous damping. c U is the Coulomb coefficient of friction; due to the relatively high sliding velocity at the contact point between the roller and the cage, u c Let it be a constant, which is 0.002.

[0097] Based on Newton's second law of motion and the established dynamic model of the roller bearing system, the dynamic differential equations for each component of the roller bearing system are as follows:

[0098] ①The differential equation of motion for the outer circle is:

[0099]

[0100] Where: m o For the outer ring mass; N oj θ represents the contact force between the rolling element and the outer ring; foj represents the frictional force between the rolling element and the outer ring; θ j Let k be the time-varying position angle of the j-th rolling element; h c h These are the stiffness coefficient and damping coefficient between the outer ring and the bearing housing, respectively. and x o and x o With y o These represent the acceleration, velocity, and displacement of the outer ring in the X and Y directions, respectively.

[0101] Figure 3To illustrate the relative positions of the rolling elements and raceways under load, dashed lines represent the initial positions of the rollers and raceways, while solid lines represent their positions under load. After the bearing is loaded, the outer ring's center of mass moves from O to O... o The inner circle's center of mass moves from O to O i The vertical and horizontal displacements of the inner ring are represented by x. i y i The vertical and horizontal displacements of the outer ring are represented by x. o y o express.

[0102] ②The differential equation of motion for the inner circle is:

[0103]

[0104] Where: m i W is the mass of the inner ring (including the shaft); N is the radial load; ij ρ is the contact force between the rolling element and the inner ring; fij is the frictional force between the rolling element and the inner ring; c is the system damping. and and These represent the acceleration and velocity of the inner ring in the X and Y directions, respectively.

[0105] ③The differential equation of cage motion is:

[0106]

[0107] In the formula: J c To maintain the moment of inertia of the cage's rotation; To maintain the angular acceleration of the cage rotation; N cj1 With N cj2 These are the impact contact forces between the rolling element and the front and rear ends of the cage pocket, respectively; R m M is the bearing pitch circle radius; c The frictional torque acting on the cage; m c To maintain rack quality; and and These represent the acceleration and velocity of the cage in the X and Y directions, respectively; G c To maintain the weight of the cage; N cx With N cy Let F be the resultant force (normal contact force and tangential friction force) of the rolling elements acting on the cage, decomposed along the X and Y axes of the inertial coordinate system; c is the system damping; F cx With F cy These are the forces decomposed into forces along the X and Y axes of the inertial coordinate system, representing the resultant force of the guide ring acting on the cage. ωc To maintain the dynamic imbalance force; To maintain the rotation angle of the cage.

[0108] Figure 4 This diagram illustrates the position and force relationship between the rolling element and the cage in an inertial frame. When the roller's motion phase leads the cage pocket phase, the roller contacts the front end of the cage; otherwise, it contacts the rear end. Where N... cj1 f cj1 These represent the contact force and frictional force between the roller and the front end of the cage, respectively, N. cj2 f cj2 These represent the contact force and friction force between the roller and the rear end of the cage, respectively.

[0109] N cx With N cy The resultant forces (normal contact force and tangential friction force) acting on the cage by the rolling elements, decomposed in the X and Y directions of the inertial coordinate axis, can be expressed as:

[0110]

[0111] F ωc To maintain the dynamic imbalance force, it can be expressed as:

[0112]

[0113] Where, m ec To maintain the mass of the frame in case of dynamic imbalance.

[0114] As a floating element in a bearing, the cage is subjected to forces from the rolling elements, lubricating oil, and guide rings, which causes the cage's center of gravity to shift. Based on the relationship between the guide clearance and the radial displacement of the cage, the interaction between the cage and the guide rings can be divided into hydrodynamic action and Hertzian contact action.

[0115] When the distance h between the cage centering surface and the outer ring guide surface is greater than 0, the cage is not in contact with the outer ring. At this time, the cage and the outer ring are mainly subjected to the hydrodynamic pressure of the lubricating oil, which can be considered as the action of a short sliding bearing. Figure 5 The relationship between the cage and the outer ring under hydrodynamic pressure is given by Oc-Xc-Yc, where Oc-Xc-Yc is the local coordinate system of the cage.

[0116] When the cage is in a hydrodynamic state, the hydrodynamic pressure acting on the centering surface of the cage can be expressed as:

[0117]

[0118] In addition, the frictional torque on the centering surface of the cage is:

[0119]

[0120] Projecting the actual hydrodynamic pressure acting on the cage onto the bearing's inertial coordinate system, it can be expressed as:

[0121]

[0122] Where u1 is the speed at which the lubricating oil is driven, u1 = R gc (ω o +ω c v1 is the relative velocity between the outer ring and the centering plane of the cage, v1 = R gc (ω o -ω c );C g It is the cage guide clearance; R gc L1 is the radius of the cage centering surface; L2 is the width of the cage centering surface; e is the cage eccentricity. ε is the offset ratio of the radial phase displacement of the cage relative to the guide gap, ε=e / C g h is the distance between the centering plane of the cage and the outer guide plane, h = C g -e.

[0123] When the distance h between the cage centering surface and the outer ring guide surface is less than or equal to 0, the cage collides with the outer ring. The interaction between the cage and the outer ring at this time is as follows: Figure 6 As shown.

[0124] The impact force and frictional force of the guide ring on the cage can be expressed as:

[0125]

[0126] Due to the lubrication friction effect, the frictional torque M acting on the cage c It can be represented as:

[0127] M c =R gc p coy

[0128] Where sign is the sign function, E c To maintain the equivalent elastic modulus of the cage and guide ring, L e To maintain the effective contact width of the cage, δ co To retain the amount of contact deformation between the cage and the guide ring, u cox The coefficient of friction between the cage and the guide ring.

[0129] Projecting the forces and moments acting on the cage onto the bearing's inertial coordinate system, we can express them as follows:

[0130]

[0131] ④ The differential equation of motion for the rolling element is:

[0132]

[0133] Where: m r G is the mass of the rolling element; r For rolling gravity; F ωj The centrifugal force of the rolling element can be expressed as: F ωj =m r R m ω rj 2 c represents the system damping. These are the accelerations of the j-th rolling element in the vertical X and horizontal Y directions of the inertial coordinate system, respectively. and Let X and Y be the velocities of the j-th rolling element along the vertical X and horizontal Y directions of the inertial coordinate system, respectively. These are the angular accelerations of the rolling element's revolution and rotation, respectively; J r The moment of inertia of the rolling element's rotation can be expressed as: J r =0.5m r R r 2 ;R r Let fcj1 be the radius of the rolling element; fcj2 and fcj3 be the frictional forces between the rolling element and the front and rear ends of the cage pocket, respectively.

[0134] The nonlinear Hertzian contact force between the rolling elements and the inner and outer raceways is related to whether the rolling elements are located in the bearing load-bearing area. The nonlinear Hertzian contact force will only occur when the rolling elements are located in the bearing load-bearing area.

[0135] Step 5: Solve the multi-degree-of-freedom dynamic differential equations using the fixed-step fourth-order Runge-Kutta method:

[0136] The parameters in the dynamic equations of each component of the cylindrical roller bearing system are determined, and the dynamic differential equations are solved using the fixed-step fourth-order Runge-Kutta method to obtain the collision force and friction force between the rolling elements and the cage.

[0137] Step 6: Use the fourth-order fixed-step Runge-Kutta method: perform iterative calculations within time t using the equation of motion. Before calculation, assign initial values ​​to the bearing system. If t has not reached the termination time T, update the relative positions of each part and set t = t + Δt, repeating S2-S7. If t reaches the termination time T, output the slippage dynamic characteristics of each bearing component at each moment, set the solution time step Δt = 5 × 10⁻⁶ s, and the solution termination time T = 2 s.

[0138] Step 7: Analysis of cage impact friction characteristics:

[0139] The amplitude, frequency, and distribution of the collision force and friction force between the rolling elements and the cage under variable speed and load conditions are analyzed.

[0140] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for analyzing the collision and friction characteristics of rolling bearings considering variable speed and load conditions, characterized in that, Includes the following steps: Step 1: Select the cylindrical roller bearing and find the bearing parameters: Step 2: Based on the dynamics theory of rolling bearings, considering the hydrodynamic pressure of the lubricating oil, the viscous damping effect between the rolling elements and the cage, and the vibration coupling effect between the outer ring and the bearing housing, a dynamic model of the cylindrical roller bearing system is established: Step 3: Based on the basic parameters of cylindrical roller bearings, considering the influence of elastohydrodynamic lubrication, calculate the stiffness and damping of the cylindrical roller bearing system using the finite element method, Hertzian contact theory, and elastohydrodynamic lubrication theory: Step 4: Consider the three degrees of freedom of the cage in planar motion and establish the multi-degree-of-freedom dynamic differential equations; Step 5: Solve the multi-degree-of-freedom dynamic differential equations using the fixed-step fourth-order Runge-Kutta method; Step 6: Use the fourth-order fixed-step Runge-Kutta method to iteratively calculate the differential equation of motion within time t; Step 7: Analyze the impact friction characteristics of the cage.

2. The method for analyzing the collision friction characteristics of rolling bearings considering variable speed and load conditions according to claim 1, characterized in that, In step 1, before performing rolling bearing dynamics modeling, it is necessary to select the cylindrical roller bearing model and find the parameters of the cylindrical roller bearing under study. The basic parameters include: outer raceway radius, inner raceway radius, pitch circle radius, number of rolling elements, rolling element diameter, radial clearance, total mass of inner ring and shaft, cage pocket clearance, cage moment of inertia, etc.

3. The method for analyzing the collision and friction characteristics of rolling bearings considering variable speed and load conditions according to claim 1, characterized in that, In step 2, the cylindrical roller bearing system is dynamically modeled using springs, damping, and concentrated mass. An equivalent spring and equivalent damper system is used to simulate the interaction between the rolling elements, raceways, and cage. The interaction between the cage and the guide raceway is considered as hydrodynamic pressure and Hertzian contact. The inner ring and shaft are considered as a whole, and the outer ring is fixed to the bearing housing. The bearing housing is considered as an elastic support with stiffness and damping. The vibration coupling effect between the outer ring and the bearing housing, the hydrodynamic pressure of the lubricating oil, and the viscous damping effect between the rolling elements and the cage are considered. Based on the rolling bearing dynamics theory, a dynamic model of the shaft-cylindrical roller bearing-bearing housing system is established.

4. The method for analyzing the collision and friction characteristics of rolling bearings considering variable speed and load conditions according to claim 1, characterized in that, In step 3, the stiffness in the roller bearing system includes: the supporting stiffness k between the bearing housing and the outer ring of the bearing. h The total contact stiffness k between the bearing outer ring and the rolling elements after elastohydrodynamic lubrication was considered. out Total contact stiffness k between the bearing inner ring and the rolling elements in Contact stiffness k between rolling elements and cage c .

5. The method for analyzing the collision friction characteristics of rolling bearings considering variable speed and load conditions according to claim 1, characterized in that, In step 4, based on Newton's second law of motion and the established dynamic model of the roller bearing system, the dynamic differential equations for each component of the roller bearing system are established as follows: ①The differential equation of motion for the outer circle is: In the formula: mo is the mass of the outer ring; Noj is the contact force between the rolling element and the outer ring; foj is the frictional force between the rolling element and the outer ring; θj is the time-varying position angle of the j-th rolling element; k h c h These are the stiffness coefficient and damping coefficient between the outer ring and the bearing housing, respectively. and and x o With y o These represent the acceleration, velocity, and displacement of the outer ring in the X and Y directions, respectively. ②The differential equation of motion for the inner circle is: Where: m i W is the mass of the inner ring (including the shaft); N is the radial load; ij ρ is the contact force between the rolling element and the inner ring; fij is the frictional force between the rolling element and the inner ring; c is the system damping. and and These represent the acceleration and velocity of the inner ring in the X and Y directions, respectively. ③The differential equation of cage motion is: In the formula: J c To maintain the moment of inertia of the cage's rotation; To maintain the angular acceleration of the cage rotation; N cj1 With N cj2 These are the impact contact forces between the rolling element and the front and rear ends of the cage pocket, respectively; R m M is the bearing pitch circle radius; c The frictional torque acting on the cage; m c To maintain rack quality; and and These represent the acceleration and velocity of the cage in the X and Y directions, respectively; G c To maintain the weight of the cage; N cx With N cy Let F be the resultant force (normal contact force and tangential friction force) of the rolling elements acting on the cage, decomposed along the X and Y axes of the inertial coordinate system; c is the system damping; F cx With F cy These are the forces decomposed into forces along the X and Y axes of the inertial coordinate system, representing the resultant force of the guide ring acting on the cage. ωc To maintain the dynamic imbalance force; To maintain the rotation angle of the cage; ④ The differential equation of motion for the rolling element is: Where: m r G is the mass of the rolling element; r For rolling gravity; F ωj c is the centrifugal force of the rolling element; c is the system damping. These are the accelerations of the j-th rolling element in the vertical X and horizontal Y directions of the inertial coordinate system, respectively. and Let X and Y be the velocities of the j-th rolling element along the vertical X and horizontal Y directions of the inertial coordinate system, respectively. These are the angular accelerations of the rolling element's revolution and rotation, respectively; J r R is the moment of inertia of the rolling element's rotation. r f is the radius of the rolling element; cj1 and f cj2 These are the frictional forces between the rolling elements and the front and rear ends of the cage pockets, respectively.

6. The method for analyzing the collision friction characteristics of rolling bearings considering variable speed and load conditions according to claim 1, characterized in that, In step 5, the parameters in the dynamic equations of each component of the cylindrical roller bearing system are determined, and the dynamic differential equations are solved using the fixed-step fourth-order Runge-Kutta method to obtain the collision force and friction force between the rolling elements and the cage.

7. The method for analyzing the collision friction characteristics of rolling bearings considering variable speed and load conditions according to claim 1, characterized in that, In step 6, the fourth-order fixed-step Runge-Kutta method is used to iteratively calculate the motion differential equation within time t. Before the calculation, the bearing system is given initial values. If t has not reached the termination time T, the relative positions of each part are updated and t = t + Δt is set. S2-S7 are repeated. If t reaches the termination time T, output the slippage dynamic characteristics of each component of the bearing at each moment. Set the time step for solving to Δt = 5 × 10⁻⁶ s, and the termination time for solving to T = 2 s.

8. The method for analyzing the collision friction characteristics of rolling bearings considering variable speed and load conditions according to claim 1, characterized in that, In step 7, the amplitude, frequency, and distribution of the collision force and friction force between the rolling elements and the cage under variable speed and load conditions are analyzed.

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